Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 588 · 40 questions

How to solve it (Divide by 7 first): Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl). Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

1. 1.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
2. 2.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
3. 3.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
4. 4.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
5. 5.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 100 sq cm (c) 600 sq cm (d) 1000 sq cm
6. 6.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
7. 7.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
8. 8.A cuboid is 9 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 63 sq cm (b) 252 sq cm (c) 81 sq cm (d) 126 sq cm
9. 9.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
10. 10.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 24 sq cm (d) 16 sq cm
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
12. 12.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 324 cu cm (c) 486 cu cm (d) 27 cu cm
13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
14. 14.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
15. 15.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
16. 16.A cuboid is 10 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 88 cu cm (b) 20 cu cm (c) 40 cu cm (d) 14 cu cm
17. 17.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 204 sq cm (b) 54 sq cm (c) 102 sq cm (d) 51 sq cm
18. 18.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
19. 19.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
20. 20.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
21. 21.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
22. 22.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
23. 23.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
24. 24.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
25. 25.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 15 cu cm (b) 12 cu cm (c) 96 cu cm (d) 136 cu cm
26. 26.A cuboid is 12 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 288 sq cm (b) 312 sq cm (c) 156 sq cm (d) 624 sq cm
27. 27.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
28. 28.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 96 sq cm (d) 97 sq cm
29. 29.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
30. 30.A cuboid is 9 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 84 sq cm (b) 168 sq cm (c) 108 sq cm (d) 336 sq cm
31. 31.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
32. 32.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 48 cu cm (b) 9 cu cm (c) 10 cu cm (d) 20 cu cm
33. 33.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 100 cu cm (c) 150 cu cm (d) 15 cu cm
34. 34.A cuboid is 8 cm long, 5 cm wide and 8 cm high. What is its total surface area? (a) 320 sq cm (b) 144 sq cm (c) 576 sq cm (d) 288 sq cm
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 616 sq cm (d) 88 sq cm
36. 36.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 36 sq cm (c) 9 sq cm (d) 27 sq cm
37. 37.A cuboid is 8 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 344 sq cm (b) 112 sq cm (c) 86 sq cm (d) 172 sq cm
38. 38.A cuboid is 12 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 48 cu cm (b) 289 cu cm (c) 22 cu cm (d) 288 cu cm
39. 39.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
40. 40.A cube has edges of 9 cm. What is its total surface area? (a) 324 sq cm (b) 729 sq cm (c) 81 sq cm (d) 486 sq cm

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